On McMullen-like mappings

Antonio Garijo, Sébastien Godillon

We introduce a generalization of the McMullen family $f_{\lambda }(z)=z^n+\lambda /z^d$. In 1988, C. McMullen showed that the Julia set of $f_{\lambda }$ is a Cantor set of circles if and only if $1/n+1/d<…